Four weeks before voters head to the polls, Catholic bishops in Minnesota have raised an issue that has largely taken a backseat to the economy and jobs this election season, renewing calls for a state constitutional amendment to ban same-sex marriage.

While such advocacy by religious groups is not uncommon, never before has the message come in the form of a DVD mailed to all Catholic households in the state. And, some say, never before has such a campaign appeared so political.

Because one candidate in the state's three-way race for governor, Republican Tom Emmer, opposes same-sex marriage, the church's message and its timing amount to an unambiguous endorsement, critics say.

The anonymous donation to the archdiocese that funded the production of more than 400,000 DVDs has also stoked questions about the proper role of religious institutions in the political process.

The "urgent message" from St. Paul-Minneapolis Archbishop John Nienstedt is that lawmakers' recent attempts to extend civil marriage rights to gays and lesbians amount to an "untested social experiment" and a "dangerous risk" to society.

Nienstedt says putting a constitutional amendment banning same-sex unions before voters is the "only way to put the one man, one woman definition of marriage beyond the reach of the courts and politicians."

Five bills introduced during the state's 2010 legislative session would legalize gay marriage. The state's new governor would play a key role in deciding whether any bill that might pass should become law.

"He's careful not to name Emmer, but it's clear Emmer's the only one who supports a constitutional amendment," said one diocesean priest who spoke with ABC News about Nienstedt's message on condition of anonymity.

Democrat Mark Dayton and Independence Party candidate Tom Horner both support same-sex marriage.

"Had it come after Nov. 2, it would have been much less political," the priest said of the church's DVD campaign. "But they're making it a hot issue, and it hasn't been a hot issue here."

Churches and non-profit groups, which are tax exempt, are permitted to advocate on issues of public policy, but they are not allowed by law to endorse specific candidates.

Church DVD Campaign: Critics Question Transparency

Gay rights advocates have cited similarities between Nienstedt's language on the DVD and political ads for Emmer by the National Organization for Marriage, which are airing simultaneously, as evidence the church is part of a coordinated effort to influence the governor's race.

"Most scandalous is that Archbishop Nienstedt has compromised his office with the use of anonymous money to fund this effort," the Rev. Michael Tegeder, pastor of the Church of St. Edward in Bloomington, wrote in a letter to the editor of the Minneapolis Star Tribune. "The constitutional amendment is a very political issue. The impression is given that political funding is at work here."

Dennis McGrath, spokesman for the Archdiocese of St. Paul and Minneapolis, told ABC News that the anonymous contribution for the campaign was "much less" than the $1 million some have alleged and that the archdiocese did not contribute "one cent" of its funds.

"We used a DVD from the Knights of Columbus and stuck on six additional minutes with the archbishop [Nienstedt]," McGrath said. "We then sent them out via non-profit bulk mail."

But Tegeder and others say the archbishop is walking a fine line, potentially imperiling the church's neutrality, if it is using financing from political groups.

Nienstedt, who says he does not know how much the DVD campaign cost or who donated the funds, insists the DVD is not political but part of an ongoing effort to educate Minnesota Catholics about marriage.

"We, and I'm particularly, are very scrupulous about not endorsing any candidate of any party," Nienstedt said in an interview with Minnesota Public Radio last week. "That's not our position. That's not our right.

"We need to bring this to the people," he said of the constitutional amendment, "rather than have it decided by the judiciary or by the legislature. ... We need to let the people say what the reality of marriage is going to be. I don't see that as that big of a political statement."

In recent years, religious groups, including the Catholic Church, have led and supported campaigns against same-sex marriage in several states, most prominently in California, where voters approved a ballot measure known as Proposition 8, banning the unions in 2008.

Thirty-one states have constitutional provisions defining marriage as between one man and one woman. Five states -- Massachusetts, Iowa, Connecticut, Vermont and New Hampshire -- and the District of Columbia perform same-sex marriages.

The Emmer campaign became a flashpoint over same-sex marriage earlier this year when Target Corp. and other prominent Minnesota-based companies donated money to a political advocacy group running ads supporting Emmer. Gay and lesbian rights groups, employees and some customers protested the donation because of Emmer's stance on same-sex marriage.